(x+4)(x-7) 3(x-7)

Jasonbradley

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Jun 16, 2024

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Factoring and Solving the Expression (x+4)(x-7) + 3(x-7)

This expression can be simplified and factored by recognizing a common factor.

1. Identify the Common Factor:

Observe that both terms in the expression share a common factor of (x - 7).

2. Factor out the Common Factor:

• Rewrite the expression by factoring out (x - 7): (x - 7) [(x + 4) + 3]

3. Simplify the Expression:

• Combine the terms inside the brackets: (x - 7) (x + 7)

4. Final Factored Form:

• The simplified and factored form of the expression is: (x - 7)(x + 7)

Solving for x:

To find the values of x that make the expression equal to zero, we can use the Zero Product Property: If the product of two factors is zero, then at least one of the factors must be zero.

• Set each factor equal to zero and solve for x:
  • x - 7 = 0 => x = 7
  • x + 7 = 0 => x = -7

Therefore, the solutions to the equation (x + 4)(x - 7) + 3(x - 7) = 0 are x = 7 and x = -7.